She said: "Because you're a woman, you're going to take this away from me?

"There's a lot of men out here that have said a lot of things, and because they are men, that doesn't happen."

Williams won the next game and continued her remonstrations - but Osaka, who displayed poise throughout, held serve to seal a win.

Image:Williams reacts after a miss to Osaka

Image:Williams received a second code violation after she smashed her racket in anger

During the presentation ceremony, there was booing from the crowd before a tearful Williams said: "I don't want to be rude. I don't want to do questions.

"I just want to tell you guys she played well. Let's make this the best moment we can and get through it and give credit where credit is due. No more booing. Let's be positive."

Osaka, also in tears, said: "I know everyone was cheering for her and I'm sorry it had to end like this. I just want to say thank you for watching the match.

"It was always my dream to play Serena in the US Open finals. I'm really glad I was able to do that."

Image:Naomi Osaka (left) and Serena Williams both broke down in tears during the trophy ceremony

Image:Despite her meltdown Williams was gracious in defeat when Osaka won the match

Speaking at a post-match news conference, Williams said she thought she was treated more harshly by the umpire than a man would have been.

"I've seen other men call other umpires several things. I'm here fighting for women's rights and for women's equality and for all kinds of stuff. For me to say 'thief,' and for him to take a game, it made me feel like it was a sexist remark. He's never taken a game from a man because they said 'thief'," Williams said.

"For me, it blows my mind. But I'm going to continue to fight for women."

(2/2) When a woman is emotional, she’s “hysterical” and she’s penalized for it. When a man does the same, he’s “outspoken” & and there are no repercussions. Thank you, @serenawilliams, for calling out this double standard. More voices are needed to do the same.

Billie Jean King, who won 12 Grand Slam singles titles and helped found the women's tennis tour and pave the way for equal prize money in the sport, backed Williams' stance.

"Several things went very wrong during the match," King tweeted. "Coaching on every point should be allowed in tennis. It isn't, and as a result, a player was penalised for the actions of her coach. This should not happen."

In a second tweet, King said: "When a woman is emotional, she's 'hysterical' and she's penalised for it. When a man does the same, he's 'outspoken' & and there are no repercussions.

"Thank you (Serena Williams) for calling out this double standard. More voices are needed to do the same."